applies a Hilbert filter with a cutoff frequency ωc to an array of data.


uses a filter kernel of length n.


applies a smoothing window wfun to the filter kernel.

Details and Options

  • HilbertFilter is used to obtain an approximation of data with a 90-degree phase shift. Data smoothing with cutoff frequency ωc reduces the susceptibility of the evaluation to signal noise with the amount of smoothing dependent on the value of the cutoff frequency ωc. Smaller values of ωc result in greater smoothing.
  • The data can be any of the following:
  • listarbitrary-rank numerical array
    tseriestemporal data such as TimeSeries and TemporalData
    imagearbitrary Image or Image3D object
    audioan Audio or Sound object
  • When applied to images and multidimensional arrays, filtering is applied successively to each dimension, starting at level 1. HilbertFilter[data,{ωc1,ωc2,}] uses the frequency ωci for the ^(th) dimension.
  • The cutoff frequency ωc should be between 0 and .
  • HilbertFilter[data,ωc] uses a filter kernel length and smoothing window suitable for the cutoff frequency ωc and the input data.
  • Typical smoothing windows wfun include:
  • BlackmanWindowsmoothing with a Blackman window
    DirichletWindowno smoothing
    HammingWindowsmoothing with a Hamming window
    {v1,v2,}use a window with values vi
    fcreate a window by sampling f between and
  • The following options can be given:
  • Padding"Fixed"the padding value to use
    SampleRateAutomaticsample rate assumed for the input
  • By default, SampleRate->1 is assumed for images as well as data. For a sampled sound object of sample rate of r, SampleRate->r is used.
  • With SampleRate->r, the cutoff frequency ωc should be between 0 and r×.


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Basic Examples  (2)

Hilbert filtering of a cosine sequence:

Click for copyable input

Hilbert filtering of an image:

Click for copyable input

Scope  (9)

Options  (5)

Applications  (1)

Properties & Relations  (4)

Possible Issues  (1)

See Also

LowpassFilter  DifferentiatorFilter  LeastSquaresFilterKernel  ListConvolve  ImageConvolve

Introduced in 2012
| Updated in 2016